Magnetic field and gradient along axis of antihelmholtz pair

[ellebee]

Homework Statement

An anti-Helmholtz pair consists of two circular coaxial current loops each with radius R and spaced a distance R apart from each other. The loops carry current I in opposite directions.
1) Calculate the magnetic field and the magnetic field gradient along the axis at the center.
2) Calculate the 1st order deviation from the value of the gradient calculated in (1) for small displacements from the center of the pair along the axis.

Homework Equations

The Attempt at a Solution

Is it not just zero?

 

[Asim Riaz]

Everywhere around the pair, there should be no net magnetic field since the two loops have equal and opposite magnetic fields. Also, the gradient should be zero since the magnitude of the magnetic field should remain constant everywhere.